Question 1

Multiply.
-$\left(-\frac{1}{5} x^{5}\right)\left(-\frac{1}{3} x^{6}\right)$

Accepted Answer

A)  $\frac{1}{8} x^{30}$ 
B)  $\frac{1}{15} \mathrm{x}^{30}$ 
C)  $\frac{1}{15} x^{11}$ 
D)  $-\frac{1}{15} x^{11}$ 
A)  $\frac{1}{8} x^{30}$ 
B)  $\frac{1}{15} \mathrm{x}^{30}$ 
C)  $\frac{1}{15} x^{11}$ 
D)  $-\frac{1}{15} x^{11}$

Question 2

Find the degree of the polynomial.
-$x^{2} y-x^{4}+5 x y-7$

Accepted Answer

A)  3 
B)  7 
C)  4 
D)  2 
A)  3 
B)  7 
C)  4 
D)  2

Question 3

Write the polynomial in two ways: with its missing terms and by leaving space for them.
-$w^{3}+6$

Accepted Answer

A)  $\begin{aligned} & w^{3}+0 w^{2}+6 \ & w^{3}+6\end{aligned}$ 
B)  $\begin{aligned} & \mathrm{w}^{3}+0 \mathrm{w}+6 \ & \mathrm{w}^{3}+6\end{aligned}$ 
C)  $w^{3}+6$
$\mathrm{w}^{3}+6$ 
D)  $\begin{aligned} & \mathrm{w}^{3}+0 \mathrm{w}^{2}+0 \mathrm{w}+6 \ & \mathrm{w}^{3}+6\end{aligned}$ 
A)  $\begin{aligned} & w^{3}+0 w^{2}+6 \ & w^{3}+6\end{aligned}$ 
B)  $\begin{aligned} & \mathrm{w}^{3}+0 \mathrm{w}+6 \ & \mathrm{w}^{3}+6\end{aligned}$ 
C)  $w^{3}+6$
$\mathrm{w}^{3}+6$ 
D)  $\begin{aligned} & \mathrm{w}^{3}+0 \mathrm{w}^{2}+0 \mathrm{w}+6 \ & \mathrm{w}^{3}+6\end{aligned}$

Question 4

Perform the division.
-$\frac{\mathrm{x}^{8}-1}{\mathrm{x}^{4}-1}$

Accepted Answer

A)  $x^{4}+12 x-1$ 
B)  $x^{4}-1$ 
C)  $x^{4}$ 
D)  $x^{4}+1$ 
A)  $x^{4}+12 x-1$ 
B)  $x^{4}-1$ 
C)  $x^{4}$ 
D)  $x^{4}+1$

Question 5

Multiply.
-$(-3 \mathrm{x}+6)(5 \mathrm{x}-3)$

Accepted Answer

A)  $2 x^{2}+39 x+39$ 
B)  $-15 x^{2}+39 x-18$ 
C)  $2 x^{2}+39 x-18$ 
D)  $-15 x^{2}+39 x+39$ 
A)  $2 x^{2}+39 x+39$ 
B)  $-15 x^{2}+39 x-18$ 
C)  $2 x^{2}+39 x-18$ 
D)  $-15 x^{2}+39 x+39$

Question 6

Multiply.
-$-4 x^{8}\left(3 x^{8}-10 x^{4}+4\right)$

Accepted Answer

A)  $-12 x^{16}+40 x^{12}+4$ 
B)  $-12 x^{16}-10 x^{4}+4$ 
C)  $-12 x^{16}+40 x^{12}-16 x^{8}$ 
D)  $-12 x^{8}+40 x^{4}-16$ 
A)  $-12 x^{16}+40 x^{12}+4$ 
B)  $-12 x^{16}-10 x^{4}+4$ 
C)  $-12 x^{16}+40 x^{12}-16 x^{8}$ 
D)  $-12 x^{8}+40 x^{4}-16$

Question 7

Identify the terms in the polynomial.
-$4 \mathrm{x}^{4}-5 \mathrm{x}^{2}-2 \mathrm{x}-2$

Accepted Answer

A)  $4 x^{4},-5 x^{2},-2 x,-2$ 
B)  $4 x^{4}, 5 x^{2}, 2 x, 2$ 
C)  $4, x^{4},-5, x^{2},-2, x,-2$ 
D)  $4, x^{4}, 5, x^{2}, 2, x, 2$ 
A)  $4 x^{4},-5 x^{2},-2 x,-2$ 
B)  $4 x^{4}, 5 x^{2}, 2 x, 2$ 
C)  $4, x^{4},-5, x^{2},-2, x,-2$ 
D)  $4, x^{4}, 5, x^{2}, 2, x, 2$

Question 8

Arrange the polynomial in descending order.
-$10+7 p^{2}+6 p^{9}-3 p^{3}+2 p$

Accepted Answer

A)  $10+2 p+7 p^{2}-3 p^{3}+6 p^{9}$ 
B)  $6 p^{9}-3 p^{3}+7 p^{2}+2 p+10$ 
C)  $7 p^{2}+2 p-3 p^{3}+6 p^{9}+10$ 
D)  $10+7 p^{2}+6 p^{9}-3 p^{3}+2 p$ 
A)  $10+2 p+7 p^{2}-3 p^{3}+6 p^{9}$ 
B)  $6 p^{9}-3 p^{3}+7 p^{2}+2 p+10$ 
C)  $7 p^{2}+2 p-3 p^{3}+6 p^{9}+10$ 
D)  $10+7 p^{2}+6 p^{9}-3 p^{3}+2 p$

Question 9

Collect like terms.
-$-8 y-5 x-3 x$

Accepted Answer

A)  $-8 y-2 x$ 
B)  $-8 y+2 x$ 
C)  -16xy 
D)  $-8 y-8 x$ 
A)  $-8 y-2 x$ 
B)  $-8 y+2 x$ 
C)  -16xy 
D)  $-8 y-8 x$

Question 10

Identify the coefficient of each term of the polynomial.
-$4 \mathrm{t}-2 \mathrm{y}-\mathrm{w}$

Accepted Answer

A)  $4,2,-1$ 
B)  $4,-2,1$ 
C)  $4,-2,-1$ 
D)  $4,2,1$ 
A)  $4,2,-1$ 
B)  $4,-2,1$ 
C)  $4,-2,-1$ 
D)  $4,2,1$

Question 11

Evaluate the polynomial.
-$y z+x y-z$ for $x=2, y=3$, and $z=4$

Accepted Answer

A)  22 
B)  14 
C)  2 
D)  18 
A)  22 
B)  14 
C)  2 
D)  18

Question 12

Multiply and simplify.
-$\mathrm{t}^{7} \cdot \mathrm{t}^{2}$

Accepted Answer

A)  $\mathrm{t}^{9}$ 
B)  $\frac{1}{t^{5}}$ 
C)  $\frac{1}{t^{9}}$ 
D)  $\mathrm{t}^{5}$ 
A)  $\mathrm{t}^{9}$ 
B)  $\frac{1}{t^{5}}$ 
C)  $\frac{1}{t^{9}}$ 
D)  $\mathrm{t}^{5}$

Question 13

Subtract.
-

Accepted Answer

A)  $7 x^{4}+6 x^{3}-x^{2}-8 x+6$ 
B)  $7 x^{4}+10 x^{3}+x^{2}-2 x$ 
C)  $7 x^{4}+10 x^{3}-x^{2}+8 x+6$ 
D)  $7 x^{4}+10 x^{3}+x^{2}-8 x+6$ 
A)  $7 x^{4}+6 x^{3}-x^{2}-8 x+6$ 
B)  $7 x^{4}+10 x^{3}+x^{2}-2 x$ 
C)  $7 x^{4}+10 x^{3}-x^{2}+8 x+6$ 
D)  $7 x^{4}+10 x^{3}+x^{2}-8 x+6$

Question 14

Write the polynomial in two ways: with its missing terms and by leaving space for them.
-$-7 \mathrm{x}^{2}$

Accepted Answer

A)  $-7 x^{2}+0 x^{0}$
$-7 x^{2}$ 
B)  $-7 x^{2}+0 x$
$-7 x^{2}$ 
C)  $-7 \mathrm{x}^{2}+0 \mathrm{x}+0 \mathrm{x}^{0}$ 
D)  None missing 
A)  $-7 x^{2}+0 x^{0}$
$-7 x^{2}$ 
B)  $-7 x^{2}+0 x$
$-7 x^{2}$ 
C)  $-7 \mathrm{x}^{2}+0 \mathrm{x}+0 \mathrm{x}^{0}$ 
D)  None missing

Question 15

Write the word or phrase that best completes each statement or answers the question.
-When is the square of the sum the sum of a square; i.e., when is $(A+B)^{2}=A^{2}+B^{2}$ ?

Accepted Answer

Now @#LAT-DLM&, so that @#LAT-DLM& just in case @#LAT-DLM&,

Question 16

Give the coefficient and degree of the term
-$-9 z$

Accepted Answer

A)  $-9,0$ 
B)  9,0 
C)  9,1 
D)  $-9,1$ 
A)  $-9,0$ 
B)  9,0 
C)  9,1 
D)  $-9,1$

Question 17

Multiply.
-$\left(\mathrm{s}-\frac{4}{7}\right)^{2}$

Accepted Answer

A)  $s^{2}-\frac{8}{49} s+\frac{16}{49}$ 
B)  $s^{2}-\frac{8}{7} s+\frac{16}{49}$ 
C)  $s^{2}-\frac{16}{7} s+\frac{16}{49}$ 
D)  $s^{2}-8 s+16$ 
A)  $s^{2}-\frac{8}{49} s+\frac{16}{49}$ 
B)  $s^{2}-\frac{8}{7} s+\frac{16}{49}$ 
C)  $s^{2}-\frac{16}{7} s+\frac{16}{49}$ 
D)  $s^{2}-8 s+16$

Question 18

Multiply.
-$\left(4 m^{2}\right)\left(3 m^{4}\right)$

Accepted Answer

A)  $-12 m^{6}$ 
B)  $12 \mathrm{~m}$ 
C)  $12 \mathrm{~m}^{6}$ 
D)  $-12 m$ 
A)  $-12 m^{6}$ 
B)  $12 \mathrm{~m}$ 
C)  $12 \mathrm{~m}^{6}$ 
D)  $-12 m$

Question 19

Multiply or divide and write scientific notation for the result.
-$\left(9.8 \times 10^{-3}\right) \div\left(2 \times 10^{-5}\right)$

Accepted Answer

A)  $4.90 \times 10^{-8}$ 
B)  $4.90 \times 10^{2}$ 
C)  $9.8 \times 10^{-8}$ 
D)  $9.8 \times 10^{2}$ 
A)  $4.90 \times 10^{-8}$ 
B)  $4.90 \times 10^{2}$ 
C)  $9.8 \times 10^{-8}$ 
D)  $9.8 \times 10^{2}$

Question 20

Add.
-$\left(x^{3} y^{2}+4 x^{2} y^{3}+3 x y+3\right)+\left(x^{2} y^{3}+4 x^{3} y^{2}+3 x y+2\right)$

Accepted Answer

A)  $5 x^{3} y^{2}+5 x^{2} y^{3}+6 x y+5$ 
B)  $3 x^{3} y^{2}+5 x^{2} y^{3}+6 x y+5$ 
C)  $2 x^{3} y^{2}+8 x^{2} y^{3}+6 x y+5$ 
D)  $5 \mathrm{x}^{3} \mathrm{y}^{2}+5 \mathrm{x}^{2} \mathrm{y}^{3}+3 \mathrm{xy}+5$ 
A)  $5 x^{3} y^{2}+5 x^{2} y^{3}+6 x y+5$ 
B)  $3 x^{3} y^{2}+5 x^{2} y^{3}+6 x y+5$ 
C)  $2 x^{3} y^{2}+8 x^{2} y^{3}+6 x y+5$ 
D)  $5 \mathrm{x}^{3} \mathrm{y}^{2}+5 \mathrm{x}^{2} \mathrm{y}^{3}+3 \mathrm{xy}+5$

Multiply. - $\left(-\frac{1}{5} x^{5}\right)\left(-\frac{1}{3} x^{6}\right)$

Find the degree of the polynomial. - $x^{2} y-x^{4}+5 x y-7$

Write the polynomial in two ways: with its missing terms and by leaving space for them. - $w^{3}+6$

Perform the division. - $\frac{\mathrm{x}^{8}-1}{\mathrm{x}^{4}-1}$

Multiply. - $(-3 \mathrm{x}+6)(5 \mathrm{x}-3)$

Multiply. - $-4 x^{8}\left(3 x^{8}-10 x^{4}+4\right)$

Identify the terms in the polynomial. - $4 \mathrm{x}^{4}-5 \mathrm{x}^{2}-2 \mathrm{x}-2$

Arrange the polynomial in descending order. - $10+7 p^{2}+6 p^{9}-3 p^{3}+2 p$

Collect like terms. - $-8 y-5 x-3 x$

Identify the coefficient of each term of the polynomial. - $4 \mathrm{t}-2 \mathrm{y}-\mathrm{w}$

Evaluate the polynomial. - $y z+x y-z$ for $x=2, y=3$ , and $z=4$

Multiply and simplify. - $\mathrm{t}^{7} \cdot \mathrm{t}^{2}$

Subtract. -

Write the polynomial in two ways: with its missing terms and by leaving space for them. - $-7 \mathrm{x}^{2}$

Write the word or phrase that best completes each statement or answers the question. -When is the square of the sum the sum of a square; i.e., when is $(A+B)^{2}=A^{2}+B^{2}$ ?

Give the coefficient and degree of the term - $-9 z$

Multiply. - $\left(\mathrm{s}-\frac{4}{7}\right)^{2}$

Multiply. - $\left(4 m^{2}\right)\left(3 m^{4}\right)$

Multiply or divide and write scientific notation for the result. - $\left(9.8 \times 10^{-3}\right) \div\left(2 \times 10^{-5}\right)$

Add. - $\left(x^{3} y^{2}+4 x^{2} y^{3}+3 x y+3\right)+\left(x^{2} y^{3}+4 x^{3} y^{2}+3 x y+2\right)$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Factoring

Rational Expressions and Equations

Systems of Equations

Radical Expressions and Equations

Quadratic Equations

Equations of Lines and Simplifying Radical Expressions

Filters

Exam 4: Polynomials: Operations

Multiply. - (−15x5)(−13x6)\left(-\frac{1}{5} x^{5}\right)\left(-\frac{1}{3} x^{6}\right)(−51​x5)(−31​x6)

Find the degree of the polynomial. - x2y−x4+5xy−7x^{2} y-x^{4}+5 x y-7x2y−x4+5xy−7

Write the polynomial in two ways: with its missing terms and by leaving space for them. - w3+6w^{3}+6w3+6

Perform the division. - x8−1x4−1\frac{\mathrm{x}^{8}-1}{\mathrm{x}^{4}-1}x4−1x8−1​

Multiply. - (−3x+6)(5x−3)(-3 \mathrm{x}+6)(5 \mathrm{x}-3)(−3x+6)(5x−3)

Multiply. - −4x8(3x8−10x4+4)-4 x^{8}\left(3 x^{8}-10 x^{4}+4\right)−4x8(3x8−10x4+4)

Identify the terms in the polynomial. - 4x4−5x2−2x−24 \mathrm{x}^{4}-5 \mathrm{x}^{2}-2 \mathrm{x}-24x4−5x2−2x−2

Arrange the polynomial in descending order. - 10+7p2+6p9−3p3+2p10+7 p^{2}+6 p^{9}-3 p^{3}+2 p10+7p2+6p9−3p3+2p

Collect like terms. - −8y−5x−3x-8 y-5 x-3 x−8y−5x−3x

Identify the coefficient of each term of the polynomial. - 4t−2y−w4 \mathrm{t}-2 \mathrm{y}-\mathrm{w}4t−2y−w

Evaluate the polynomial. - yz+xy−zy z+x y-zyz+xy−z for x=2,y=3x=2, y=3x=2,y=3 , and z=4z=4z=4

Multiply and simplify. - t7⋅t2\mathrm{t}^{7} \cdot \mathrm{t}^{2}t7⋅t2